# Full text of "Analytical Mechanics"

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```CHAPTER IX. ENERGY.
150. Results of Work. — Consider the work done by t! engine of a train in pulling it upgrade. The work done m: be divided into three parts:
(a)  Work done against frictional forces.
(b)  Work done against gravitational forces.
(c)  Work done against the kinetic reaction.
The result of work done against frictional forces is hes The amount of heat generated is proportional to the amou of work done. The heat may be utilized, at least theore cally, to do work. Thus a part, if not all, of the origir work may be recovered.
The apparent result of the work done against the gra^ tational forces is the elevation of the train to a higher lev The work done may be recovered by letting the train cor down to its former level and thereby do work. Therefo the work done against gravitational forces may be consider to be stored up.
The apparent result of the work done against the kinel reaction in accelerating the train is an increase in the v locity of the train.    The work done may be recovered 1 letting the train overcome a force, which tends to redu the velocity of the train to its original value.    Therefore this case also the work done may be said to have be< stored up.     In fact in all three cases the work done stored up.    In the first case, however, work is not availafc as readily as in the other two cases.    In order to conve
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